1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 210,393 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 210,383 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      7
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      1
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      1
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      0
## 168   2020-08-15          East of England      1
## 169   2020-03-01                   London      0
## 170   2020-03-02                   London      0
## 171   2020-03-03                   London      0
## 172   2020-03-04                   London      0
## 173   2020-03-05                   London      0
## 174   2020-03-06                   London      1
## 175   2020-03-07                   London      0
## 176   2020-03-08                   London      0
## 177   2020-03-09                   London      1
## 178   2020-03-10                   London      0
## 179   2020-03-11                   London      5
## 180   2020-03-12                   London      6
## 181   2020-03-13                   London     10
## 182   2020-03-14                   London     13
## 183   2020-03-15                   London      9
## 184   2020-03-16                   London     15
## 185   2020-03-17                   London     23
## 186   2020-03-18                   London     27
## 187   2020-03-19                   London     25
## 188   2020-03-20                   London     44
## 189   2020-03-21                   London     49
## 190   2020-03-22                   London     54
## 191   2020-03-23                   London     63
## 192   2020-03-24                   London     86
## 193   2020-03-25                   London    112
## 194   2020-03-26                   London    129
## 195   2020-03-27                   London    129
## 196   2020-03-28                   London    122
## 197   2020-03-29                   London    145
## 198   2020-03-30                   London    149
## 199   2020-03-31                   London    181
## 200   2020-04-01                   London    202
## 201   2020-04-02                   London    191
## 202   2020-04-03                   London    197
## 203   2020-04-04                   London    231
## 204   2020-04-05                   London    195
## 205   2020-04-06                   London    197
## 206   2020-04-07                   London    220
## 207   2020-04-08                   London    239
## 208   2020-04-09                   London    206
## 209   2020-04-10                   London    171
## 210   2020-04-11                   London    178
## 211   2020-04-12                   London    158
## 212   2020-04-13                   London    166
## 213   2020-04-14                   London    143
## 214   2020-04-15                   London    142
## 215   2020-04-16                   London    140
## 216   2020-04-17                   London    100
## 217   2020-04-18                   London    101
## 218   2020-04-19                   London    103
## 219   2020-04-20                   London     96
## 220   2020-04-21                   London     94
## 221   2020-04-22                   London    109
## 222   2020-04-23                   London     77
## 223   2020-04-24                   London     71
## 224   2020-04-25                   London     58
## 225   2020-04-26                   London     53
## 226   2020-04-27                   London     51
## 227   2020-04-28                   London     44
## 228   2020-04-29                   London     45
## 229   2020-04-30                   London     40
## 230   2020-05-01                   London     41
## 231   2020-05-02                   London     41
## 232   2020-05-03                   London     36
## 233   2020-05-04                   London     30
## 234   2020-05-05                   London     25
## 235   2020-05-06                   London     37
## 236   2020-05-07                   London     37
## 237   2020-05-08                   London     30
## 238   2020-05-09                   London     23
## 239   2020-05-10                   London     26
## 240   2020-05-11                   London     18
## 241   2020-05-12                   London     18
## 242   2020-05-13                   London     17
## 243   2020-05-14                   London     20
## 244   2020-05-15                   London     18
## 245   2020-05-16                   London     14
## 246   2020-05-17                   London     15
## 247   2020-05-18                   London     11
## 248   2020-05-19                   London     14
## 249   2020-05-20                   London     19
## 250   2020-05-21                   London     12
## 251   2020-05-22                   London     10
## 252   2020-05-23                   London      6
## 253   2020-05-24                   London      7
## 254   2020-05-25                   London      9
## 255   2020-05-26                   London     14
## 256   2020-05-27                   London      7
## 257   2020-05-28                   London      8
## 258   2020-05-29                   London      7
## 259   2020-05-30                   London     12
## 260   2020-05-31                   London      6
## 261   2020-06-01                   London     10
## 262   2020-06-02                   London      8
## 263   2020-06-03                   London      6
## 264   2020-06-04                   London      8
## 265   2020-06-05                   London      4
## 266   2020-06-06                   London      0
## 267   2020-06-07                   London      5
## 268   2020-06-08                   London      5
## 269   2020-06-09                   London      5
## 270   2020-06-10                   London      8
## 271   2020-06-11                   London      5
## 272   2020-06-12                   London      3
## 273   2020-06-13                   London      3
## 274   2020-06-14                   London      3
## 275   2020-06-15                   London      1
## 276   2020-06-16                   London      2
## 277   2020-06-17                   London      1
## 278   2020-06-18                   London      2
## 279   2020-06-19                   London      5
## 280   2020-06-20                   London      3
## 281   2020-06-21                   London      4
## 282   2020-06-22                   London      2
## 283   2020-06-23                   London      1
## 284   2020-06-24                   London      4
## 285   2020-06-25                   London      3
## 286   2020-06-26                   London      2
## 287   2020-06-27                   London      1
## 288   2020-06-28                   London      2
## 289   2020-06-29                   London      2
## 290   2020-06-30                   London      1
## 291   2020-07-01                   London      2
## 292   2020-07-02                   London      2
## 293   2020-07-03                   London      2
## 294   2020-07-04                   London      1
## 295   2020-07-05                   London      3
## 296   2020-07-06                   London      2
## 297   2020-07-07                   London      1
## 298   2020-07-08                   London      3
## 299   2020-07-09                   London      4
## 300   2020-07-10                   London      0
## 301   2020-07-11                   London      1
## 302   2020-07-12                   London      1
## 303   2020-07-13                   London      1
## 304   2020-07-14                   London      0
## 305   2020-07-15                   London      2
## 306   2020-07-16                   London      0
## 307   2020-07-17                   London      0
## 308   2020-07-18                   London      2
## 309   2020-07-19                   London      0
## 310   2020-07-20                   London      0
## 311   2020-07-21                   London      1
## 312   2020-07-22                   London      0
## 313   2020-07-23                   London      2
## 314   2020-07-24                   London      0
## 315   2020-07-25                   London      1
## 316   2020-07-26                   London      0
## 317   2020-07-27                   London      1
## 318   2020-07-28                   London      0
## 319   2020-07-29                   London      0
## 320   2020-07-30                   London      0
## 321   2020-07-31                   London      0
## 322   2020-08-01                   London      0
## 323   2020-08-02                   London      2
## 324   2020-08-03                   London      0
## 325   2020-08-04                   London      0
## 326   2020-08-05                   London      0
## 327   2020-08-06                   London      1
## 328   2020-08-07                   London      0
## 329   2020-08-08                   London      0
## 330   2020-08-09                   London      0
## 331   2020-08-10                   London      0
## 332   2020-08-11                   London      1
## 333   2020-08-12                   London      0
## 334   2020-08-13                   London      1
## 335   2020-08-14                   London      0
## 336   2020-08-15                   London      0
## 337   2020-03-01                 Midlands      0
## 338   2020-03-02                 Midlands      0
## 339   2020-03-03                 Midlands      1
## 340   2020-03-04                 Midlands      0
## 341   2020-03-05                 Midlands      0
## 342   2020-03-06                 Midlands      0
## 343   2020-03-07                 Midlands      0
## 344   2020-03-08                 Midlands      2
## 345   2020-03-09                 Midlands      1
## 346   2020-03-10                 Midlands      0
## 347   2020-03-11                 Midlands      2
## 348   2020-03-12                 Midlands      6
## 349   2020-03-13                 Midlands      5
## 350   2020-03-14                 Midlands      4
## 351   2020-03-15                 Midlands      5
## 352   2020-03-16                 Midlands     11
## 353   2020-03-17                 Midlands      8
## 354   2020-03-18                 Midlands     13
## 355   2020-03-19                 Midlands      8
## 356   2020-03-20                 Midlands     28
## 357   2020-03-21                 Midlands     13
## 358   2020-03-22                 Midlands     31
## 359   2020-03-23                 Midlands     33
## 360   2020-03-24                 Midlands     41
## 361   2020-03-25                 Midlands     48
## 362   2020-03-26                 Midlands     64
## 363   2020-03-27                 Midlands     72
## 364   2020-03-28                 Midlands     89
## 365   2020-03-29                 Midlands     92
## 366   2020-03-30                 Midlands     90
## 367   2020-03-31                 Midlands    123
## 368   2020-04-01                 Midlands    140
## 369   2020-04-02                 Midlands    142
## 370   2020-04-03                 Midlands    124
## 371   2020-04-04                 Midlands    151
## 372   2020-04-05                 Midlands    164
## 373   2020-04-06                 Midlands    140
## 374   2020-04-07                 Midlands    123
## 375   2020-04-08                 Midlands    186
## 376   2020-04-09                 Midlands    139
## 377   2020-04-10                 Midlands    127
## 378   2020-04-11                 Midlands    142
## 379   2020-04-12                 Midlands    139
## 380   2020-04-13                 Midlands    120
## 381   2020-04-14                 Midlands    116
## 382   2020-04-15                 Midlands    147
## 383   2020-04-16                 Midlands    102
## 384   2020-04-17                 Midlands    118
## 385   2020-04-18                 Midlands    115
## 386   2020-04-19                 Midlands     92
## 387   2020-04-20                 Midlands    107
## 388   2020-04-21                 Midlands     86
## 389   2020-04-22                 Midlands     78
## 390   2020-04-23                 Midlands    103
## 391   2020-04-24                 Midlands     79
## 392   2020-04-25                 Midlands     72
## 393   2020-04-26                 Midlands     81
## 394   2020-04-27                 Midlands     74
## 395   2020-04-28                 Midlands     68
## 396   2020-04-29                 Midlands     53
## 397   2020-04-30                 Midlands     56
## 398   2020-05-01                 Midlands     64
## 399   2020-05-02                 Midlands     51
## 400   2020-05-03                 Midlands     52
## 401   2020-05-04                 Midlands     61
## 402   2020-05-05                 Midlands     59
## 403   2020-05-06                 Midlands     59
## 404   2020-05-07                 Midlands     48
## 405   2020-05-08                 Midlands     34
## 406   2020-05-09                 Midlands     37
## 407   2020-05-10                 Midlands     42
## 408   2020-05-11                 Midlands     33
## 409   2020-05-12                 Midlands     45
## 410   2020-05-13                 Midlands     40
## 411   2020-05-14                 Midlands     38
## 412   2020-05-15                 Midlands     40
## 413   2020-05-16                 Midlands     34
## 414   2020-05-17                 Midlands     31
## 415   2020-05-18                 Midlands     36
## 416   2020-05-19                 Midlands     35
## 417   2020-05-20                 Midlands     36
## 418   2020-05-21                 Midlands     32
## 419   2020-05-22                 Midlands     27
## 420   2020-05-23                 Midlands     34
## 421   2020-05-24                 Midlands     20
## 422   2020-05-25                 Midlands     26
## 423   2020-05-26                 Midlands     33
## 424   2020-05-27                 Midlands     29
## 425   2020-05-28                 Midlands     28
## 426   2020-05-29                 Midlands     20
## 427   2020-05-30                 Midlands     21
## 428   2020-05-31                 Midlands     22
## 429   2020-06-01                 Midlands     20
## 430   2020-06-02                 Midlands     22
## 431   2020-06-03                 Midlands     24
## 432   2020-06-04                 Midlands     16
## 433   2020-06-05                 Midlands     21
## 434   2020-06-06                 Midlands     20
## 435   2020-06-07                 Midlands     17
## 436   2020-06-08                 Midlands     16
## 437   2020-06-09                 Midlands     18
## 438   2020-06-10                 Midlands     15
## 439   2020-06-11                 Midlands     13
## 440   2020-06-12                 Midlands     12
## 441   2020-06-13                 Midlands      6
## 442   2020-06-14                 Midlands     18
## 443   2020-06-15                 Midlands     12
## 444   2020-06-16                 Midlands     15
## 445   2020-06-17                 Midlands     11
## 446   2020-06-18                 Midlands     15
## 447   2020-06-19                 Midlands     10
## 448   2020-06-20                 Midlands     15
## 449   2020-06-21                 Midlands     14
## 450   2020-06-22                 Midlands     14
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## 452   2020-06-24                 Midlands     15
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## 454   2020-06-26                 Midlands      5
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## 458   2020-06-30                 Midlands      6
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## 460   2020-07-02                 Midlands     10
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## 462   2020-07-04                 Midlands      4
## 463   2020-07-05                 Midlands      6
## 464   2020-07-06                 Midlands      5
## 465   2020-07-07                 Midlands      3
## 466   2020-07-08                 Midlands      5
## 467   2020-07-09                 Midlands      9
## 468   2020-07-10                 Midlands      3
## 469   2020-07-11                 Midlands      0
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## 471   2020-07-13                 Midlands      1
## 472   2020-07-14                 Midlands      1
## 473   2020-07-15                 Midlands      6
## 474   2020-07-16                 Midlands      2
## 475   2020-07-17                 Midlands      3
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## 479   2020-07-21                 Midlands      1
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## 599   2020-06-03 North East and Yorkshire     23
## 600   2020-06-04 North East and Yorkshire     17
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## 602   2020-06-06 North East and Yorkshire     21
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## 604   2020-06-08 North East and Yorkshire     11
## 605   2020-06-09 North East and Yorkshire     12
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## 609   2020-06-13 North East and Yorkshire     10
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## 612   2020-06-16 North East and Yorkshire     10
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## 614   2020-06-18 North East and Yorkshire     11
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## 618   2020-06-22 North East and Yorkshire      7
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## 622   2020-06-26 North East and Yorkshire      7
## 623   2020-06-27 North East and Yorkshire      4
## 624   2020-06-28 North East and Yorkshire      5
## 625   2020-06-29 North East and Yorkshire      2
## 626   2020-06-30 North East and Yorkshire      7
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## 629   2020-07-03 North East and Yorkshire      4
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## 957   2020-06-25               South East      5
## 958   2020-06-26               South East      8
## 959   2020-06-27               South East      9
## 960   2020-06-28               South East      6
## 961   2020-06-29               South East      5
## 962   2020-06-30               South East      5
## 963   2020-07-01               South East      2
## 964   2020-07-02               South East      8
## 965   2020-07-03               South East      3
## 966   2020-07-04               South East      6
## 967   2020-07-05               South East      5
## 968   2020-07-06               South East      4
## 969   2020-07-07               South East      6
## 970   2020-07-08               South East      3
## 971   2020-07-09               South East      7
## 972   2020-07-10               South East      3
## 973   2020-07-11               South East      4
## 974   2020-07-12               South East      4
## 975   2020-07-13               South East      5
## 976   2020-07-14               South East      5
## 977   2020-07-15               South East      6
## 978   2020-07-16               South East      3
## 979   2020-07-17               South East      1
## 980   2020-07-18               South East      5
## 981   2020-07-19               South East      2
## 982   2020-07-20               South East      6
## 983   2020-07-21               South East      4
## 984   2020-07-22               South East      2
## 985   2020-07-23               South East      3
## 986   2020-07-24               South East      1
## 987   2020-07-25               South East      1
## 988   2020-07-26               South East      3
## 989   2020-07-27               South East      0
## 990   2020-07-28               South East      3
## 991   2020-07-29               South East      2
## 992   2020-07-30               South East      3
## 993   2020-07-31               South East      1
## 994   2020-08-01               South East      2
## 995   2020-08-02               South East      3
## 996   2020-08-03               South East      0
## 997   2020-08-04               South East      0
## 998   2020-08-05               South East      0
## 999   2020-08-06               South East      0
## 1000  2020-08-07               South East      0
## 1001  2020-08-08               South East      1
## 1002  2020-08-09               South East      0
## 1003  2020-08-10               South East      1
## 1004  2020-08-11               South East      0
## 1005  2020-08-12               South East      1
## 1006  2020-08-13               South East      0
## 1007  2020-08-14               South East      0
## 1008  2020-08-15               South East      0
## 1009  2020-03-01               South West      0
## 1010  2020-03-02               South West      0
## 1011  2020-03-03               South West      0
## 1012  2020-03-04               South West      0
## 1013  2020-03-05               South West      0
## 1014  2020-03-06               South West      0
## 1015  2020-03-07               South West      0
## 1016  2020-03-08               South West      0
## 1017  2020-03-09               South West      0
## 1018  2020-03-10               South West      0
## 1019  2020-03-11               South West      1
## 1020  2020-03-12               South West      0
## 1021  2020-03-13               South West      0
## 1022  2020-03-14               South West      1
## 1023  2020-03-15               South West      0
## 1024  2020-03-16               South West      0
## 1025  2020-03-17               South West      2
## 1026  2020-03-18               South West      2
## 1027  2020-03-19               South West      4
## 1028  2020-03-20               South West      3
## 1029  2020-03-21               South West      6
## 1030  2020-03-22               South West      7
## 1031  2020-03-23               South West      8
## 1032  2020-03-24               South West      7
## 1033  2020-03-25               South West      9
## 1034  2020-03-26               South West     11
## 1035  2020-03-27               South West     13
## 1036  2020-03-28               South West     21
## 1037  2020-03-29               South West     18
## 1038  2020-03-30               South West     23
## 1039  2020-03-31               South West     23
## 1040  2020-04-01               South West     21
## 1041  2020-04-02               South West     23
## 1042  2020-04-03               South West     30
## 1043  2020-04-04               South West     42
## 1044  2020-04-05               South West     32
## 1045  2020-04-06               South West     34
## 1046  2020-04-07               South West     39
## 1047  2020-04-08               South West     47
## 1048  2020-04-09               South West     24
## 1049  2020-04-10               South West     46
## 1050  2020-04-11               South West     43
## 1051  2020-04-12               South West     23
## 1052  2020-04-13               South West     27
## 1053  2020-04-14               South West     24
## 1054  2020-04-15               South West     32
## 1055  2020-04-16               South West     29
## 1056  2020-04-17               South West     33
## 1057  2020-04-18               South West     25
## 1058  2020-04-19               South West     31
## 1059  2020-04-20               South West     26
## 1060  2020-04-21               South West     26
## 1061  2020-04-22               South West     23
## 1062  2020-04-23               South West     17
## 1063  2020-04-24               South West     19
## 1064  2020-04-25               South West     15
## 1065  2020-04-26               South West     27
## 1066  2020-04-27               South West     13
## 1067  2020-04-28               South West     17
## 1068  2020-04-29               South West     15
## 1069  2020-04-30               South West     26
## 1070  2020-05-01               South West      6
## 1071  2020-05-02               South West      7
## 1072  2020-05-03               South West     10
## 1073  2020-05-04               South West     17
## 1074  2020-05-05               South West     14
## 1075  2020-05-06               South West     19
## 1076  2020-05-07               South West     16
## 1077  2020-05-08               South West      6
## 1078  2020-05-09               South West     11
## 1079  2020-05-10               South West      5
## 1080  2020-05-11               South West      8
## 1081  2020-05-12               South West      7
## 1082  2020-05-13               South West      7
## 1083  2020-05-14               South West      6
## 1084  2020-05-15               South West      4
## 1085  2020-05-16               South West      4
## 1086  2020-05-17               South West      6
## 1087  2020-05-18               South West      4
## 1088  2020-05-19               South West      6
## 1089  2020-05-20               South West      1
## 1090  2020-05-21               South West      9
## 1091  2020-05-22               South West      7
## 1092  2020-05-23               South West      6
## 1093  2020-05-24               South West      3
## 1094  2020-05-25               South West      8
## 1095  2020-05-26               South West     11
## 1096  2020-05-27               South West      5
## 1097  2020-05-28               South West     10
## 1098  2020-05-29               South West      7
## 1099  2020-05-30               South West      3
## 1100  2020-05-31               South West      2
## 1101  2020-06-01               South West      7
## 1102  2020-06-02               South West      2
## 1103  2020-06-03               South West      7
## 1104  2020-06-04               South West      2
## 1105  2020-06-05               South West      2
## 1106  2020-06-06               South West      1
## 1107  2020-06-07               South West      3
## 1108  2020-06-08               South West      3
## 1109  2020-06-09               South West      0
## 1110  2020-06-10               South West      1
## 1111  2020-06-11               South West      2
## 1112  2020-06-12               South West      2
## 1113  2020-06-13               South West      2
## 1114  2020-06-14               South West      0
## 1115  2020-06-15               South West      2
## 1116  2020-06-16               South West      2
## 1117  2020-06-17               South West      0
## 1118  2020-06-18               South West      0
## 1119  2020-06-19               South West      0
## 1120  2020-06-20               South West      2
## 1121  2020-06-21               South West      0
## 1122  2020-06-22               South West      1
## 1123  2020-06-23               South West      1
## 1124  2020-06-24               South West      1
## 1125  2020-06-25               South West      0
## 1126  2020-06-26               South West      3
## 1127  2020-06-27               South West      0
## 1128  2020-06-28               South West      0
## 1129  2020-06-29               South West      1
## 1130  2020-06-30               South West      0
## 1131  2020-07-01               South West      0
## 1132  2020-07-02               South West      0
## 1133  2020-07-03               South West      0
## 1134  2020-07-04               South West      0
## 1135  2020-07-05               South West      1
## 1136  2020-07-06               South West      0
## 1137  2020-07-07               South West      0
## 1138  2020-07-08               South West      2
## 1139  2020-07-09               South West      0
## 1140  2020-07-10               South West      1
## 1141  2020-07-11               South West      0
## 1142  2020-07-12               South West      0
## 1143  2020-07-13               South West      1
## 1144  2020-07-14               South West      0
## 1145  2020-07-15               South West      0
## 1146  2020-07-16               South West      0
## 1147  2020-07-17               South West      1
## 1148  2020-07-18               South West      0
## 1149  2020-07-19               South West      0
## 1150  2020-07-20               South West      0
## 1151  2020-07-21               South West      0
## 1152  2020-07-22               South West      0
## 1153  2020-07-23               South West      0
## 1154  2020-07-24               South West      0
## 1155  2020-07-25               South West      0
## 1156  2020-07-26               South West      0
## 1157  2020-07-27               South West      0
## 1158  2020-07-28               South West      0
## 1159  2020-07-29               South West      0
## 1160  2020-07-30               South West      1
## 1161  2020-07-31               South West      0
## 1162  2020-08-01               South West      0
## 1163  2020-08-02               South West      0
## 1164  2020-08-03               South West      0
## 1165  2020-08-04               South West      0
## 1166  2020-08-05               South West      0
## 1167  2020-08-06               South West      0
## 1168  2020-08-07               South West      0
## 1169  2020-08-08               South West      0
## 1170  2020-08-09               South West      0
## 1171  2020-08-10               South West      0
## 1172  2020-08-11               South West      0
## 1173  2020-08-12               South West      0
## 1174  2020-08-13               South West      0
## 1175  2020-08-14               South West      0
## 1176  2020-08-15               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-08-16"

The completion date of the NHS Pathways data is Sunday 16 Aug 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -17.038   -6.483   -1.536    3.976   11.184  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.267e+00  7.663e-02   55.68   <2e-16 ***
## note_lag    1.725e-05  7.995e-07   21.57   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 39.24201)
## 
##     Null deviance: 20489.9  on 106  degrees of freedom
## Residual deviance:  4480.3  on 105  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   71.303918    1.000017
exp(confint(lag_mod))
##                 2.5 %    97.5 %
## (Intercept) 61.172377 82.615949
## note_lag     1.000016  1.000019

Rsq(lag_mod)
## [1] 0.7813412

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.6.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.6.0: Sun Jul  5 00:43:10 PDT 2020; root:xnu-6153.141.1~9/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                          "Mac-1597658969024.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.2     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.15             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.2.0       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.2      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.1          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.1          tibble_3.0.3         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.5.0          webshot_0.5.2     httr_1.4.2       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.7       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-9         zip_2.1.0         magrittr_1.5      kyotil_2019.11-22
## [41] Matrix_1.2-18     Rcpp_1.0.5        munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.6      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.13.0 modelr_0.1.8      vctrs_0.3.2       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.16        
## [77] openxlsx_4.1.5    broom_0.7.0       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1